4. Show that the norm on l0 given by I| (11, .., In...) |lo= sup{|r;| : j= 1,2, ...} can not be given by a scalar product.

Suppose f is the function defined by f(x) = Ax, where a. The domain of f is b. The codomain of f is 24 0 DA. OB. OC. OD. DE. OF. A = 0 1 8 3 -3 0 2 -1 5 For instance, enter R^5 for R5. For instance, enter R^5 for R5. c. Select all of the vectors that are in the kernel of f. You should be able to justify your answers (there may be more than one correct answer DA. OB. OC. D. DE. F. d. Select all of the vectors that are in the image of f. You should be able to justify your answers (there may be more than one correct answer).

9. Let r = = (i, 5, 1 + i) be vectors in C. Compute (r, y), ||z||, ||y||, and ||r+ y|. Then verify both the Cauchy-Schwarz inequality and the triangle inequality. (-4,2 + i, 1), and y

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